"Education is not the filling of a pail, but the lighting of a fire." – As W. B. Yeats never said

I quite like the Minecraft computer game. I like the way that players build something of their own rather than chase after the limited objective of most games. I hadn’t realised that Minecraft was owned by Microsoft through a subsidiary but, if I had, this wouldn’t bother me.

Education is often characterised by a debate between those who favour child-centred methods and those who prefer a teacher-led approach. I’ve noticed a tendency of the former to accuse the latter of being in cahoots with big business. They point, for instance, to Pearson and its role in testing. But business is really just there to provide stuff that people will buy. For every company selling us tests and textbooks there will be one selling Minecraft as an engaging activity that you can guide students through from the side. Business is neutral. It is up to us as a profession to decide if, when and how to use these products.

Microsoft has an Australian Twitter account dedicated to education. This account recently tweeted a link to a blog post by an English teacher about how he uses Minecraft to create ‘immersive engagement’. I responded to this:

This is relatively mild criticism. Notice that I link to my own post on engagement being a poor proxy for learning. So this isn’t just snarkiness: I have a certain amount of thinking to support my scepticism. It is possible that using Minecraft to teach English results in highly engaged individuals who are motivated by the game scenario but who are not learning much English.

To be fair, the author of the blog post does suggest that the use of Minecraft led to better writing. I just find it hard to see why this would be the case. If students are spending time building stuff in the Minecraft world then they are not thinking about writing or constructing an argument. There may well be elements of narrative that are addressed by assuming particular roles but that’s still not the main activity.

It reminds me of the activity that Dan Willingham outlined in ‘Why don’t students like school?’ Students were meant to be learning about the Underground Railroad – a route used to escape slavery in the Southern U.S. The escapees often baked and ate biscuits and so the class teacher thought this would be an engaging activity to do. The problem was that this caused students to think about flour and water and baking times rather than the Underground Railroad.

I also think that the idea that we should motivate students through engaging activities and that this will lead to learning places the cart before the horse. We know that people are motivated by mastery: getting better at writing will motivate students about writing. If we focus on mastery then we need to focus on the teaching strategies that most directly address a student’s ability to write.

You may have noticed something odd about the screen-grab above. The tweet by @MSAUedu that I am responding to does not appear embedded in my own tweet. This is because the Microsoft account has now blocked me, presumably for this single interaction. So Microsoft want to engage our students with Minecraft but they don’t appear to be interested in engaging in a discussion about the value of this.

Dan Meyer recently published a blog post on how to teach the idea that any number raised to the power of zero is simply one. This is an important result that crops up in many different areas and so it’s critical that students know it.

Meyer asked us to choose between two strategies. The first he described as ‘teaching tricks’ and I agree that it’s not very enlightening. The presenter of the video simply tells you that anything raised to the power of zero is one. And that’s it.

Meyer is keen on a different pattern-based activity that he describes as ‘sensemaking’. I think this approach is better than the first but it still doesn’t really explain anything. In my view, it’s more of a pattern-based trick. I’m not quite sure what ‘sensemaking’ means – which is ironic – but I thought this would be a good cue to explain the way that I would teach the concept.

The first important point is that I think this needs to be taught over and over again to students of different ages, whenever exponentials arise. So I’ve taught it in Years 8, 9, 10, 11 and 12. With older students studying Maths Methods – our abstract maths course – I would rely more on pronumerals in the explanation although I would still always illustrate with natural numbers.

Secondly, this would be a small part of my explanation of index laws rather than something that sits on its own. I just see the power of zero as an interesting result.

And I haven’t worked any of this out myself – it comes from an amalgam of textbook explanations, discussions with colleagues and so on. So this is not the patent Ashman method.

Prior knowledge

As ever with mathematics, there are some things that students need to understand in order to grasp the explanation. I won’t outline how I would teach these underpinning ideas because that might make the post rather long. Suffice it to say that there would be a process like the one I’m about to describe. It would be critical that they understood the following three points and so I would check this through questioning:

1. Fractions can be composed and decomposed in the following way (I might also discuss non-examples involving sums):

2. Indices are a shorthand for repeated multiplication of the same term:

3. Any number divided by itself is one – I usually remind students of this by saying something like, “How many fives [point to denominator] are there in five [point to numerator]”:

This enables us to work out some laws for indices. I would explicitly lead students through one of these and I would pepper the exposition with questions to the students as I went along. I don’t ask for them to raise their hands – as far as my students are concerned, I call on them randomly – and I tend to ask them to work out any of the component parts that relate to prior knowledge.

I would start by looking at something like this result:

With younger students, I would give a couple more examples with natural numbers and with older ones I might use a pronumeral such as ‘a’. To make it simple, I’d have more repeated terms in the numerator than denominator. The fact that we can then partner up each term on the bottom with one on the top means that, in order to get the final power, we can do a subtraction of the two original powers. This is similar to one of the ways that subtraction is explained to students in earlier number work.

As an aside, you might think that I should talk about ‘canceling’ here and I certainly introduce the shorthand of canceling at some point. However, I tend to persist with the kind of decomposition I’ve used above for a quite a while so that students can see where canceling comes from – even if I fade it out and only go through the whole process every third or fourth example. At this point, I might not rewrite as separate quotients but still talk of ‘three divided by three is one’ as I draw my cancelling lines through the terms.

I don’t think you can avoid the error of over-generalisation that many students eventually make that leads them to cancelling the two in an expression like this:

However, when they do this you can return them to decomposition as an explanation of why that doesn’t work.

Back to the original point, we have now derived a rule that looks something like this:

This is incredibly powerful and should also lead to a discussion and some examples and exercises that include negative powers, but that’s not the objective here.

Armed with this rule, we can reverse engineer a zero power. How can we construct one? Well, ‘m‘ and ‘n‘ would need to be equal:

If the students really need convincing then you can give a few more examples just to show that it always comes out as one.

I also use index laws to show the equivalence of fractional powers and roots.

Universal Design for Learning (UDL) has been on my radar since a piece in The Conversation cited UDL research in a discussion of differentiation.

The citation immediately struck me as odd. Take a look. There are a series of papers listed that seem to show that providing students with choice is a good idea. Then, as Pedro de Bruyckere points out, there is a request for more evidence, “Do you have additional evidence to support this Checkpoint? Tell us!”

This does not represent the standard approach to science which, if anything, should seek disconfirming evidence (here’s a review paper critical of student choice, for instance).

If you look on ERIC for peer reviewed studies of UDL you will find few that test its effectiveness in terms of the learning of students. This entry is fairly typical and describes a trial to see how well teachers who were trained in UDL then implemented its principles.

Neuroscience

The UDL Center appears to be the main website providing information to teachers (although it also links to the CAST site). According to the UDL Center:

“Individuals bring a huge variety of skills, needs, and interests to learning. Neuroscience reveals that these differences are as varied and unique as our DNA or fingerprints. Three primary brain networks come into play.”

It then goes on to list these three networks as: ‘recognition networks’, ‘strategic networks’ and ‘affective networks’. Each of these is illustrated by a picture of a brain with a different area coloured-in.

We should be pretty sceptical at this point. I’ve written before about the way that neuroscience is sometimes used to justify particular teaching methods and I recently came across a paper by Jeffrey Bowers that makes this case much better than me.

Bowers explains that neuroscience is often used to support claims that are trivially true, such as that we learn less well under stress, and claims that have already been established through basic psychology research, such as the efficacy of phonics instruction. Neuroscience is also sometimes used to support practices in ways that are unwarranted. To Bowers, neuroscience has so far added nothing of use to teachers and is unlikely to do so in the future.

This seems true of the way that neuroscience is used to support UDL. The claim that we should use multiple representations of material seems either trivially true or known to us via psychology (although there are good and bad ways of doing this). The claim that we need to give students choices of how to act, express themselves and engage with content might be unwarranted.

Accommodate or address?

Bowers discusses the case where we find that a particular learning issue is linked to abnormal responses in a certain part of the brain. He asks what we should do about this: should we work on developing the functions associated with that brain part or should we look to develop workarounds? Neuroscience cannot tell us.

I would characterise this as the fundamental question of differentiation: do we accommodate the difference or do we address it?

Clearly, if a student is blind then we cannot expect him to read visual text. We have no choice but to accommodate the disability and offer an alternative.

But we can fall into error if we extend this logic to a student who has difficulty writing. Do we give her the option of recording her thoughts as an audio file? This would provide her with a different means of expression that she may prefer, given the difficulties she has with writing and particularly if sanctioned and encouraged by teachers. Yet this won’t address her writing difficulty. She will never improve at writing if she avoids writing. And she will fall further behind her peers who are practising more writing than her.

Perhaps this represents the difference between a disability and some other form of difficulty: the former must be accommodated but the latter should probably be addressed.

Books

I have only dipped my toes in the water of UDL. The websites recommend various books. Perhaps these offer clear guidance on how to avoid some of the potential pitfalls. However, the invocation of neuroscience is at best unhelpful. And if teachers who just dip in their toes like me go away with the message that students should be offered lots of choice in how to complete activities then there is potential for harm.

A song came on the radio the other day; a silly and trivial pop song. As the first few clunky bars bounced out of my car speakers, I found myself gripped and confounded by a wave of overwhelming nostalgia. The song was ‘Things can only get better’ by D:Ream.

The Labour Party picked the tune as its theme for the 1997 British election. I hated the choice at the time. Why not something by Oasis? Perhaps, ‘Some might say’? Why choose a chirpy bubblegum pop song instead?

I now know the answer. The song was not for me. I physically ached for a change of government having only ever known The Conservatives in charge. Town centres had be ravaged by recession and public services were decaying. Privatised monopolies raked in cash while refusing to invest. I had signed a Socialist Worker Party petition against the Conservatives’ Criminal Justice Bill which effectively banned outdoor raves, characterised as they were by music containing ‘a series of repetitive beats’. The government obsessed over these kinds of illiberal social laws while the economy stagnated. I was ready for a different lot of politicians.

At the age of 16 I was convinced that Labour would win. But the 1992 election was lost to John Major, his stupid soapbox and a scare campaign about Labour’s tax plans. It was the ordinary people who had been frightened into voting Tory in 1992 that Labour needed to reassure and a silly, optimistic pop song was a small part of that.

“Things can only get better,” went the refrain and people up and down the land nodded their heads and thought, “what have we got to lose?”

In May 1997 I was in my final month of university. We had an election night party. The polls had been looking good but, after 1992, we took nothing for granted. We nervously clutched our beers in a room in College where we had rigged up a TV. And we waited.

By the time Michael Portillo fell, we started to realise just what a big Labour win was in the offing. We cheered and hugged each other. We cried. A guy on the floor below complained to the porters about the noise we were making and they came round and half-heartedly asked us to drop the volume a little, leaving us in no doubt at all about where their sympathies lay.

I started training as a teacher and entered my first classroom in October of 1997.

Back then, education was a Cindarella service. School buildings were run down. Budgets were tight. The new Labour government brought extra funding and schools were rebuilt, even if the Private Finance initiative seemed an odd way to do it, storing up problems for the future.

In time, I grew disillusioned. New Labour could never live up to the promise of that May evening. We had university tuition fees that I thought were wrong and the asymmetric impact of which made me question the devolution settlement between Britain’s constituent countries. Then Iraq came.

Even in education, Labour moved from sensible policies such as the national strategies to encouraging the diobolical energies of a thousand consultants who wanted to sell us learning styles and thinking skills.

But things really did get better. That promise was honoured.

And I suppose I’m sad because I reflect on the Labour Party today and realise that they have learnt nothing. If Jeremy Corbyn were to choose a theme tune then it would be Billy Bragg singing ‘Between the Wars’ whilst sat on a sack of coal.

We’ve probably all heard a colleague say something like, “I did a great activity today. It worked well. The kids were really engaged.” We even have professional development based on this premise: A consultant will come in to a school and promote a drama-based activity or project-based learning and everyone will conclude how effective it is because the students are really engaged.

I think the term ‘engagement’ has two meanings when people use it in this way. The first is that students are motivated by the activity and the second is that they are actively doing something. Perhaps the latter is seen to imply to the former because, in many classrooms, full participation in the activity might be optional.

Professor Robert Coe claims that engagement is a poor proxy for learning.

Source: Professor Robert Coe

It is important to understand what ‘poor proxy’ means. It doesn’t mean that engagement is undesirable or in conflict with learning. Rather, learning is invisible. It’s not something that we can directly observe. So if we want to conclude that learning has taken place then we look for a proxy. A good proxy might be something like a delayed test. If students score well then we can infer that learning has taken place. Coe is claiming that engagement is a poor proxy.

This is quite reasonable. We can imagine students busily and enthusiastically doing stuff but learning little; or at least learning little of what is intended. For instance, a Macbeth diorama could engage students for hours without improving their ability to analyse the play.

We can also imagine students staring pretty blankly while a teacher talks and yet learning loads. Certainly, the mind has to be active for learning to take place but this doesn’t mean that the body has to be physically doing something. Richard Mayer calls the conflation of the two the, ‘constructivist teaching fallacy‘.

So why has Coe’s perfectly sensible suggestion provoked so much argument on Twitter recently?

Let’s take another of Coe’s poor proxies: classroom is ordered, calm, under control. I view an orderly classroom as highly desirable. I think that, in many cases, it is a necessary prerequisite for learning to occur. But I would not argue that we can infer from an orderly classroom that learning is taking place. Students could be behaving very well and learning little. Conversely, it is quite possible for students to be learning whilst some members of the class are misbehaving.

In my first year of teaching I had a difficult Year 10 science class for 80 minutes on a Friday afternoon. If we worked hard for the first 40 minutes I let the students research a science topic in the computer room for the last 40 minutes. They learnt little science from this research but many teachers dropped by and commented on how well behaved the students were.

I think that the problem people have with Coe’s analysis is that much of the evaluation of educational innovations never gets past the question of whether students are engaged. If this engagement leads to better learning then we could and should use better proxies to measure this learning. If a consultant comes in to your school and tries to sell you engagement then the professional response should be to ask for something more.

Regular readers of this blog will know that I have written a number of times about Reading Recovery. Reading Recovery research is exemplary in the way that it illustrates the problems with unfair tests.

Reading Recovery is a one-to-one intervention. When compared to doing nothing (or doing something short of one-to-one tuition) it appears to be effective. The problem is that we don’t know whether this is due to the form of the intervention or its nature. Would students make similar progress with a program of any additional one-to-one reading tuition of similar duration or is it the specific Reading Recovery strategies that cause the effect?

Theoretically, Reading Recovery is perhaps unsound. It is based upon the whole language approach to reading prevalent in the 1970s when it was developed. Although it has latterly incorporated an element of phonics, it’s not clear that this is the systematic synthetic phonics supported by research. And it still uses the three-cuing system criticised by Jim Rose in his report for the UK government.

I recently read a review that showed that the size of the effect when Reading Recovery is compared to do nothing/little is smaller than when systematic phonics intervention programs are compared with do nothing/little. This is strongly suggestive of the need to switch away from Reading Recovery to systematic phonics interventions.

A recent review for the New South Wales government took a look at the available evidence, including long term effects, and found a lack of support for Reading Recovery. The New South Wales government have now announced that they will cease to mandate Reading Recovery as the intervention of choice in government schools.

About this time in the Northern hemisphere, as teachers settle into a pattern with new classes and norms have been set, there will be many who are struggling to manage behaviour.

There are three statements that I wish to make about classroom management and that I believe to be true.

1. Classroom management exists as a separate set of skills to the other skills involved in teaching, even if there is considerable overlap.

2. Some people are really good at classroom management and others are poor at it. You can get better at it by working hard on it and some people will make progress more rapidly than others. In other words, learning classroom management is exactly the same as learning any other set of skills.

3. Classroom management exists in a school context. You can’t surf if there are no waves and you can’t manage a classroom without support from the whole school community, particularly the leadership.

Unfortunately, student-centred education is to varying degrees the dominant philosophy in our education systems and it struggles to reconcile itself with any of this. Student-centred educators valorise intrinsic motivation. They see classroom management as extrinsic motivation at best and as a form of coercion at worst.

The problem is that, by definition, you can’t intrinsically motivate students. It has to come from within. Even posing an interesting question for students to investigate is, ultimately, a form of external manipulation. If you give students plenty of choice over what to do and how to do it then those students who are already intrinsically motivated about academic work will pursue it and those who are not will not. And what are you going to do about it? This is a pedagogy of privilege where those who already have a lot will gain more and those who are without will gain little. Think of the child who isn’t taught to read because she’s not considered ready and then imagine how that will play out in the long term.

If student-centred educators accepted this logic then they would need to change their philosophy. So they cling to a myth instead. If only the content can be made interesting enough, relevant enough, authentic enough, then all students will want to engage: we can extrinsically intrinsically motivate children. This is also a convenient cover for managers who don’t want to intervene to help teachers deal with behaviour issues – it’s the teacher’s fault for presenting dull lessons. She should perhaps spend a few extra hours a day designing funky activities.

Although a myth, there are aspects of this approach that are plausible. I have written before that I would back myself to engage most middle school science classes by giving them poster work to do, particularly if I didn’t insist on there being much science content on the posters.

But I haven’t actually changed students’ motivation. I’ve change my own objective of teaching science into something else that students are already motivated about: bubble writing and drawing pictures. Similarly, I can change my maths teaching objective from teaching students algebra to getting them to play with piles of sticks and form patterns. Students might be more motivated by this than actual algebra (or they might perhaps start throwing the sticks around).

It is true, of course, that there are more and less interesting ways of presenting a concept. Given the choice, I would pick the more interesting one, provided that it doesn’t reduce the clarity of what I’m trying to teach or subtly shift my objective. But this is still about externally manipulating the situational interest of students rather than changing what intrinsically motivates them.

Ultimately, classroom management reduces to the manipulation of rewards and sanctions coupled with cues and warnings; extrinsic motivation. These can be as subtle as a look or an encouraging word and the can be as radical as exclusion from school. I believe that exclusion has to be available as an ultimate sanction – some students can be a danger to their peers – but I do wonder whether incidents often escalate to the level of exclusion because a systematic approach is not in place prior to this stage.

This issue could present in the form of a new teacher whose relationship deteriorates with her class, gets little support and ends up saying something that prompts a child to push her against a wall, leading to an exclusion. It could look like the student who is never coerced into engaging in academic work, sees the gap between himself and his peers grow ever wider and becomes angry and resentful. These are two examples of the challenges that breed an environment where students are lost to education and teachers decide to quit the profession.

We can avoid this situation and we know how. We need to abandon the student-centred philosophy with its queasiness about classroom management.